Proof step e-7b68ca495e98f7ea

basis_map A007318 → concludes about basis_map_A007318 of Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*4^j. JSON

Theorem

Geometric basis map (elementary) polytool ?

Operation

Image under a basis map u^k -> P_k

{
  "map": "A007318",
  "operation": "basis_map"
}

Premises

• Triangle whose (i,j)-th entry is binomial(i,j)*12^(i-j)*4^j. (sequence)
  uses: Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]

Claims

• { "claim": "real_rooted", "from_index": 0, "region": { "upper": { "closed": true, "value": "0" } } }

Verification and certificate

• polytool: replayed (the certificate replayed when the step was written)
• Lean: not attempted
• certificate: basis_map, SHA-256 a26f30629f707353de1f475feb8d2ab32dceb0c8cc1cbf3f2b4216bd7e5e3c3e, 6,922 bytes (1,410 compressed); download JSON

Cited by

• n-ee879560f84ab2b6 (real_rooted)
• n-ee879560f84ab2b6 (one_signed_coefficients)
• n-ee879560f84ab2b6 (hadamard_kernel)